{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from matplotlib.colors import LogNorm\n",
    "from mpl_toolkits.mplot3d import axes3d, Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def computeCost(X, y, theta):  # 代价函数\n",
    "    inner = np.power((np.dot(X, theta.T) - y), 2)\n",
    "    return np.sum(inner) / (2 * len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "path = '../data/ex1data1.txt'\n",
    "data = pd.read_csv(path, header=None, names=['Population', 'Profit'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Population   Profit\n",
       "0      6.1101  17.5920\n",
       "1      5.5277   9.1302\n",
       "2      8.5186  13.6620\n",
       "3      7.0032  11.8540\n",
       "4      5.8598   6.8233"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Population</th>\n",
       "      <th>Profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>97.000000</td>\n",
       "      <td>97.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>8.159800</td>\n",
       "      <td>5.839135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.869884</td>\n",
       "      <td>5.510262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>5.026900</td>\n",
       "      <td>-2.680700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.707700</td>\n",
       "      <td>1.986900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.589400</td>\n",
       "      <td>4.562300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>8.578100</td>\n",
       "      <td>7.046700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>22.203000</td>\n",
       "      <td>24.147000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Population     Profit\n",
       "count   97.000000  97.000000\n",
       "mean     8.159800   5.839135\n",
       "std      3.869884   5.510262\n",
       "min      5.026900  -2.680700\n",
       "25%      5.707700   1.986900\n",
       "50%      6.589400   4.562300\n",
       "75%      8.578100   7.046700\n",
       "max     22.203000  24.147000"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(figsize=(12,8))\n",
    "ax.scatter(data.Population,data.Profit)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.insert(0, 'ones', 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "cols = data.shape[1]\n",
    "X = data.iloc[:, 0:cols - 1]\n",
    "y = data.iloc[:, cols - 1:cols]\n",
    "X = np.matrix(X.values)\n",
    "y = np.matrix(y.values)\n",
    "theta = np.matrix(np.array([0, 0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32.072733877455676"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computeCost(X, y, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientDescent(X,y,theta,alpha,iters):\n",
    "    tmp = np.matrix(np.zeros(theta.shape)) #初始化的1x2临时矩阵\n",
    "    cost = np.zeros(iters) #初始不同的θ组合对应的J（θ）\n",
    "    m = X.shape[0] #数据的组数即X矩阵的行数\n",
    "    for i in range(iters): #迭代iters次\n",
    "        tmp = theta - ( alpha / m )*( X * theta.T - y ).T * X\n",
    "        #X（97，2），theta.T（2，1），y（97，1）\n",
    "        theta = tmp\n",
    "        cost[i] = computeCost(X,y,theta)\n",
    "    return theta,cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-3.24140214  1.1272942 ]] <class 'numpy.matrix'>\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4.515955503078912"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha = 0.01\n",
    "iters = 1000\n",
    "\n",
    "final_theta,cost = gradientDescent(X,y,theta,alpha,iters)\n",
    "print(final_theta,type(final_theta))\n",
    "computeCost(X, y,final_theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalEqn(X,y):\n",
    "    theta = np.linalg.inv(X.T@X)@X.T@y\n",
    "    return theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-3.89578088]\n",
      " [ 1.19303364]] <class 'numpy.matrix'>\n",
      "-3.89578087831188 1.1930336441895955\n"
     ]
    }
   ],
   "source": [
    "final_theta = normalEqn(X,y)\n",
    "print(final_theta,type(final_theta))\n",
    "print(final_theta[0,0],final_theta[1,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(data.Population.min(),data.Population.max(),100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# f = final_theta[0, 0] + (final_theta[0, 1] * x)\n",
    "f = final_theta[0,0] + (final_theta[1,0] * x)\n",
    "fig, ax = plt.subplots(figsize=(12,8)) #调整画布的大小\n",
    "ax.plot(x, f, 'r', label='Prediction') #画预测的直线 并标记左上角的标签\n",
    "ax.scatter(data.Population, data.Profit, label='Traning Data') #画真实数据的散点图 并标记左上角的标签\n",
    "ax.legend(loc=2) #显示标签\n",
    "ax.set_xlabel('Population') #设置横轴标签\n",
    "ax.set_ylabel('Profit')\n",
    "ax.set_title('Predicted Profit vs. Population Size') #设置正上方标题\n",
    "plt.show() #显示图像"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.plot(np.arange(iters),cost,color='r')\n",
    "\n",
    "ax.set_xlabel('Iterations')\n",
    "ax.set_ylabel('Cost')\n",
    "ax.set_title(\"Error vs. Training Epoch\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 利用库的知识\n",
    "from sklearn import linear_model\n",
    "model = linear_model.LinearRegression()\n",
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array(X[:, 1].A1)\n",
    "f = model.predict(X).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.plot(x, f, 'r', label='Prediction')\n",
    "ax.scatter(data.Population, data.Profit, label='Traning Data')\n",
    "ax.legend(loc=2)\n",
    "ax.set_xlabel('Population')\n",
    "ax.set_ylabel('Profit')\n",
    "ax.set_title('Predicted Profit vs. Population Size')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/dist-packages/matplotlib/contour.py:1243: UserWarning: No contour levels were found within the data range.\n",
      "  warnings.warn(\"No contour levels were found\"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ===================== Part 3: Visualizing J(theta0, theta1) =====================\n",
    "\n",
    "theta0_vals = np.linspace(-10, 10, 100)\n",
    "theta1_vals = np.linspace(-1, 4, 100)\n",
    "\n",
    "xs, ys = np.meshgrid(theta0_vals, theta1_vals)\n",
    "J_vals = np.zeros(xs.shape)\n",
    "# Fill out J_vals\n",
    "for i in range(0, theta0_vals.size):\n",
    "    for j in range(0, theta1_vals.size):\n",
    "        t = np.array([theta0_vals[i], theta1_vals[j]])\n",
    "        J_vals[i][j] = computeCost(X, y, t)\n",
    "\n",
    "J_vals = np.transpose(J_vals)\n",
    "# 三维图\n",
    "fig1 = plt.figure(1)\n",
    "ax = fig1.gca(projection='3d')\n",
    "ax.plot_surface(xs, ys, J_vals)\n",
    "plt.xlabel(r'$\\theta_0$')\n",
    "plt.ylabel(r'$\\theta_1$')\n",
    "# 等高线图\n",
    "plt.figure(2)\n",
    "lvls = np.logspace(-2, 3, 20)\n",
    "plt.contour(xs, ys, J_vals, levels=lvls, norm=LogNorm())\n",
    "plt.plot(final_theta[0,0], final_theta[1,0], c='r', marker=\"x\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting Data...\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running Gradient Descent...\n",
      "Initial cost: 32.072733877455676(This value should be about 32.07\n",
      "Theta found by gradient descent:[-3.63029144  1.16636235]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Program paused. Press ENTER to continue \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For population=35,000,we predict a profit of 4519.768(This value should be about 4519.77)\n",
      "For population = 70,000, we predict a profit of 45342.450 (This value should be about 45342.45)\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Program paused. Press ENTER to continue \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Visualizing J(theta_0,theta_1)...\n",
      "100\n",
      "100\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/dist-packages/matplotlib/contour.py:1000: UserWarning: The following kwargs were not used by contour: 'normal'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.colors import LogNorm\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "def plot_data(x,y):\n",
    "    plt.scatter(x,y,marker='x',s=50,c='r',alpha=0.8)\n",
    "    plt.xlabel('population')\n",
    "    plt.ylabel('profits')\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "def h(X,theta):\n",
    "    return X.dot(theta)\n",
    "def compute_cost(X,y,theta):\n",
    "    m=y.size\n",
    "    prediction=h(X,theta)\n",
    "    # cost=sum(np.power(prediction-y,2))/(2*m)\n",
    "    cost = (prediction - y).dot(prediction - y) / (2 * m)\n",
    "    return cost\n",
    "def gradient_descent(X,y,theta,alpha,num_iters):\n",
    "    m=y.size\n",
    "    J_history=np.zeros(num_iters)\n",
    "    for i in range(0,num_iters):\n",
    "        # theta=theta-(alpha/m)*sum((h(X,theta)-y).dot(X))\n",
    "        theta=theta-(alpha/m)*(h(X,theta)-y).dot(X)\n",
    "        J_history[i]=compute_cost(X,y,theta)\n",
    "\n",
    "    return theta,J_history\n",
    "    \n",
    "print('Plotting Data...')\n",
    "data=np.loadtxt('../data/ex1data1.txt',delimiter=',')#加载txt格式数据集 每一行以“，”分隔\n",
    "\n",
    "X=data[:,0]\n",
    "y=data[:,1]\n",
    "\n",
    "m=y.size\n",
    "\n",
    "plt.figure(0)\n",
    "plot_data(X,y)\n",
    "# input()\n",
    "\n",
    "print('Running Gradient Descent...')\n",
    "X=np.c_[np.ones(m),X]\n",
    "theta=np.zeros(2)\n",
    "\n",
    "iterations=1500\n",
    "alpha=0.01\n",
    "print('Initial cost: '+str(compute_cost(X,y,theta))+'(This value should be about 32.07')\n",
    "theta,J_history =gradient_descent(X,y,theta,alpha,iterations)\n",
    "print('Theta found by gradient descent:'+str(theta.reshape(2)))\n",
    "\n",
    "plt.figure(0)\n",
    "line1, =plt.plot(X[:,1],np.dot(X,theta),label='Linear Regression')\n",
    "plot_data(X[:,1],y)\n",
    "plt.legend(handles=[line1])\n",
    "\n",
    "input('Program paused. Press ENTER to continue')\n",
    "\n",
    "predict1=np.dot(np.array([1,3.5]),theta)\n",
    "print('For population=35,000,we predict a profit of {:0.3f}(This value should be about 4519.77)'.format(predict1*10000))\n",
    "predict2=np.dot(np.array([1,7]),theta)\n",
    "print('For population = 70,000, we predict a profit of {:0.3f} (This value should be about 45342.45)'.format(predict2*10000))\n",
    "input('Program paused. Press ENTER to continue')\n",
    "\n",
    "print('Visualizing J(theta_0,theta_1)...')\n",
    "theta0_vals=np.linspace(-10,10,100)\n",
    "theta1_vals=np.linspace(-1,4,100)\n",
    "J_vals=np.zeros((theta0_vals.shape[0],theta1_vals.shape[0]))\n",
    "print(theta0_vals.shape[0])\n",
    "print(theta1_vals.shape[0])\n",
    "\n",
    "\n",
    "for i in range(0,theta0_vals.shape[0]):\n",
    "    for j in range(0,theta1_vals.shape[0]):\n",
    "        t=np.array([theta0_vals[i],theta1_vals[j]])\n",
    "        J_vals[i][j]=compute_cost(X,y,t)\n",
    "J_vals=np.transpose(J_vals)\n",
    "fig=plt.figure(1)\n",
    "ax=Axes3D(fig)\n",
    "xs,ys=np.meshgrid(theta0_vals,theta1_vals)\n",
    "plt.title(\"Visualizing J(theta_0,theta_1)\")\n",
    "\n",
    "ax.plot_surface(xs,ys,J_vals)\n",
    "ax.set_xlabel('$\\theta_0$',color='r')\n",
    "ax.set_ylabel('$\\theta_1$',color='r')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "plt.figure(2)\n",
    "lvls=np.logspace(-2,3,20)\n",
    "plt.contourf(xs,ys,J_vals,10,levels=lvls,normal=LogNorm())\n",
    "\n",
    "plt.plot(theta[0], theta[1], c='r', marker=\"x\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ploting Data...\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running Gradient Descent...\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/dist-packages/numpy/core/_methods.py:38: RuntimeWarning: overflow encountered in reduce\n",
      "  return umr_sum(a, axis, dtype, out, keepdims, initial, where)\n",
      "/home/jovyan/.virtualenvs/basenv/lib/python3.7/site-packages/ipykernel_launcher.py:9: RuntimeWarning: overflow encountered in power\n",
      "  if __name__ == '__main__':\n",
      "/home/jovyan/.virtualenvs/basenv/lib/python3.7/site-packages/ipykernel_launcher.py:17: RuntimeWarning: invalid value encountered in subtract\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta found by gradient descent:\n",
      " [[nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      "  nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      "  nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      "  nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      "  nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      "  nan nan nan nan nan nan nan]\n",
      " [nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      "  nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      "  nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      "  nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      "  nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      "  nan nan nan nan nan nan nan]] \n",
      "\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "x and y must have same first dimension, but have shapes (97, 1) and (1, 97)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-38-326ec863d634>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     48\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     49\u001b[0m \u001b[0;31m# plot the linear fit\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 50\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'bo'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmarkersize\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     51\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Population of City in 10,000s'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     52\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mylabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Profit in $10,000s'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   2809\u001b[0m     return gca().plot(\n\u001b[1;32m   2810\u001b[0m         *args, scalex=scalex, scaley=scaley, **({\"data\": data} if data\n\u001b[0;32m-> 2811\u001b[0;31m         is not None else {}), **kwargs)\n\u001b[0m\u001b[1;32m   2812\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2813\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/matplotlib/__init__.py\u001b[0m in \u001b[0;36minner\u001b[0;34m(ax, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1808\u001b[0m                         \u001b[0;34m\"the Matplotlib list!)\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mlabel_namer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1809\u001b[0m                         RuntimeWarning, stacklevel=2)\n\u001b[0;32m-> 1810\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1811\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1812\u001b[0m         inner.__doc__ = _add_data_doc(inner.__doc__,\n",
      "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/matplotlib/axes/_axes.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(self, scalex, scaley, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1609\u001b[0m         \u001b[0mkwargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmlines\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLine2D\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_alias_map\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1610\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1611\u001b[0;31m         \u001b[0;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1612\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1613\u001b[0m             \u001b[0mlines\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36m_grab_next_args\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    391\u001b[0m                 \u001b[0mthis\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    392\u001b[0m                 \u001b[0margs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 393\u001b[0;31m             \u001b[0;32myield\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    394\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    395\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36m_plot_args\u001b[0;34m(self, tup, kwargs)\u001b[0m\n\u001b[1;32m    368\u001b[0m             \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    369\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 370\u001b[0;31m         \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_xy_from_xy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    371\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    372\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcommand\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'plot'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36m_xy_from_xy\u001b[0;34m(self, x, y)\u001b[0m\n\u001b[1;32m    229\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    230\u001b[0m             raise ValueError(\"x and y must have same first dimension, but \"\n\u001b[0;32m--> 231\u001b[0;31m                              \"have shapes {} and {}\".format(x.shape, y.shape))\n\u001b[0m\u001b[1;32m    232\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    233\u001b[0m             raise ValueError(\"x and y can be no greater than 2-D, but have \"\n",
      "\u001b[0;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (97, 1) and (1, 97)"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD6CAYAAACvZ4z8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAC3NJREFUeJzt28+L3Xe9x/Hn6xJLatQhyR1QIhWl0ErBLDqCmFbI9CYgRsGd1IDiIlAQRIhC/wXJpqAg2UmIuFUDpcQk4A9a6swi4aIWifVCNjIhkLjQKcjbRQ6Mnjud8z1nzpyJ7z4fm35m5p3Mez6ZPHsY8k1VIUnq67/2ewFJ0t4y9JLUnKGXpOYMvSQ1Z+glqTlDL0nNDQp9kvcl+fkOHz+Y5EqSm0kuJcn8VpQk7cbE0Cd5HFgHTu0wdha4U1XHgcMTZiVJCzQx9FX1t6r6FHBnh7FV4OrofB04OYfdJElzcGBOv89R4P7o/AB4anwgyTngHMChQ4eeffrpp+f0qSXpvWF9ff1uVS1P++vmFfq7wNLovDR6+99U1UXgIsDKykqtra3N6VNL0ntDkv+b5dfN61/dXANOj86rwI05/b6SpF2aOvRJPp7kwti7LwPHktwC7vEw/JKkR8DgH91U1ZOj/74NnB/72CZwZr6rSZLmwQemJKk5Qy9JzRl6SWrO0EtSc4Zekpoz9JLUnKGXpOYMvSQ1Z+glqTlDL0nNGXpJas7QS1Jzhl6SmjP0ktScoZek5gy9JDVn6CWpOUMvSc0ZeklqztBLUnOGXpKaM/SS1Jyhl6TmDL0kNWfoJak5Qy9JzRl6SWrO0EtSc4Zekpoz9JLUnKGXpOYMvSQ1Z+glqTlDL0nNGXpJas7QS1JzE0Of5GCSK0luJrmUJNvMHEry0yS/SfK9vVlVkjSLIa/ozwJ3quo4cBg4tc3MV4E3quoE8EyST85xR0nSLgwJ/SpwdXS+DpzcZmYTeP/o1f5B4J35rCdJ2q0hoT8K3B+dHwBHtpn5MfB54PfAH6rq9vhAknNJ1pKsbWxszLqvJGlKQ0J/F1ganZdGb497GfhhVT0NHEny2fGBqrpYVStVtbK8vDzzwpKk6QwJ/TXg9Oi8CtzYZuaDwN9H503gA7tfTZI0D0NCfxk4luQWcA+4neTC2MwPgJeSvA48zsP/OUiSHgEHJg1U1SZwZuzd58dm/gycmN9akqR58YEpSWrO0EtSc4Zekpoz9JLUnKGXpOYMvSQ1Z+glqTlDL0nNGXpJas7QS1Jzhl6SmjP0ktScoZek5gy9JDVn6CWpOUMvSc0ZeklqztBLUnOGXpKaM/SS1Jyhl6TmDL0kNWfoJak5Qy9JzRl6SWrO0EtSc4Zekpoz9JLUnKGXpOYMvSQ1Z+glqTlDL0nNGXpJas7QS1Jzhl6SmpsY+iQHk1xJcjPJpSR5l7nvJvlVkleTPDb/VSVJsxjyiv4scKeqjgOHgVPjA0k+ATxTVc8DrwIfneuWkqSZDQn9KnB1dL4OnNxm5gXgcJJfAs8Db89nPUnSbg0J/VHg/uj8ADiyzcwysFFVn+Phq/nnxgeSnEuylmRtY2Nj1n0lSVMaEvq7wNLovDR6e9wD4K3R+U/AsfGBqrpYVStVtbK8vDzLrpKkGQwJ/TXg9Oi8CtzYZmYd+PTo/CQPYy9JegQMCf1l4FiSW8A94HaSC/86UFWvA3eT/BZ4q6renP+qkqRZHJg0UFWbwJmxd5/fZu6leS0lSZofH5iSpOYMvSQ1Z+glqTlDL0nNGXpJas7QS1Jzhl6SmjP0ktScoZek5gy9JDVn6CWpOUMvSc0ZeklqztBLUnOGXpKaM/SS1Jyhl6TmDL0kNWfoJak5Qy9JzRl6SWrO0EtSc4Zekpoz9JLUnKGXpOYMvSQ1Z+glqTlDL0nNGXpJas7QS1Jzhl6SmjP0ktScoZek5gy9JDVn6CWpOUMvSc1NDH2Sg0muJLmZ5FKS7DD77SS/mO+KkqTdGPKK/ixwp6qOA4eBU9sNJfkY8PX5rSZJmochoV8Fro7O14GT7zL3CvDyPJaSJM3PkNAfBe6Pzg+AI+MDSV4EbgK/e7ffJMm5JGtJ1jY2NmbZVZI0gyGhvwssjc5Lo7fHnQFeAH4CPJvkm+MDVXWxqlaqamV5eXnWfSVJUxoS+mvA6dF5FbgxPlBVL1bVc8BXgPWq+v78VpQk7caQ0F8GjiW5BdwDbie5sLdrSZLm5cCkgara5OGPZv7V+XeZ/TPwP7tfS5I0Lz4wJUnNGXpJas7QS1Jzhl6SmjP0ktScoZek5gy9JDVn6CWpOUMvSc0ZeklqztBLUnOGXpKaM/SS1Jyhl6TmDL0kNWfoJak5Qy9JzRl6SWrO0EtSc4Zekpoz9JLUnKGXpOYMvSQ1Z+glqTlDL0nNGXpJas7QS1Jzhl6SmjP0ktScoZek5gy9JDVn6CWpOUMvSc0ZeklqztBLUnM7hj7JwSRXktxMcilJtplJkh8leSPJz5Ic2Lt1JUnTmvSK/ixwp6qOA4eBU9vMnAAOVNVngA8Bp+e7oiRpNyaFfhW4OjpfB05uM/MX4JXR+Z057SVJmpNJP2Y5CtwfnR8AT40PVNUfAZJ8GXgMeG273yjJOeAcwBNPPDHjupKkaU16RX8XWBqdl0Zv/z9JvgR8C/hiVf1ju5mqulhVK1W1sry8POu+kqQpTQr9NbZ+5r4K3BgfSPJh4DvAF6rqr/NdT5K0W5NCfxk4luQWcA+4neTC2MzXgI8AryX5dZJv7MGekqQZpaoW/klXVlZqbW1t4Z9Xkv6TJVmvqpVpf50PTElSc4Zekpoz9JLUnKGXpOYMvSQ1Z+glqTlDL0nNGXpJas7QS1Jzhl6SmjP0ktScoZek5gy9JDVn6CWpOUMvSc0ZeklqztBLUnOGXpKaM/SS1Jyhl6TmDL0kNWfoJak5Qy9JzRl6SWrO0EtSc4Zekpoz9JLUnKGXpOYMvSQ1Z+glqTlDL0nNGXpJas7QS1Jzhl6SmjP0ktScoZek5nYMfZKDSa4kuZnkUpLMMiNJ2j+TXtGfBe5U1XHgMHBqxhlJ0j6ZFPpV4OrofB04OeOMJGmfHJjw8aPA/dH5AfDUjDMkOQecG725meR/p1u1rf8G7u73Eo8I72KLd7HFu9iybV8nmRT6u8DS6LzE9pc9ZIaqughcBEiyVlUrU2/bkHexxbvY4l1s8S62JFmb5ddN+tHNNeD06LwK3JhxRpK0TyaF/jJwLMkt4B5wO8mFCTPX5r+mJGlWO/7opqo2gTNj7z4/YGaSi1POd+ZdbPEutngXW7yLLTPdRapq3otIkh4hPhkrSc3tWeh9qnbLwLtIkh8leSPJz5JM+hdR/5Gm+TNP8u0kv1jkfos09C6SfDfJr5K8muSxRe+5CAP/jhxK8tMkv0nyvf3Yc1GSvC/Jz3f4+FTt3MtX9D5Vu2XI13kCOFBVnwE+xNa/ZOpm0J95ko8BX1/gXvth4l0k+QTwTFU9D7wKfHSxKy7MkO+LrwJvVNUJ4Jkkn1zkgouS5HFgnZ17OFU79zL0PlW7ZcjX+RfgldH5nUUstU+G/pm/Ary8kI32z5C7eAE4nOSXwPPA2wvabdGG3MUm8P7Rq9eDNP17UlV/q6pPAXd2GJuqnXsZ+vEnZo/MONPBxK+zqv5YVW8m+TLwGPDaAvdbpIl3keRF4CbwuwXutR+GfP8vAxtV9Tkevpp/bkG7LdqQu/gx8Hng98Afqur2gnZ7FE3Vzr0M/dyeqm1g0NeZ5EvAt4AvVtU/FrTbog25izM8fCX7E+DZJN9c0G6LNuQuHgBvjc5/Ao4tYK/9MOQuXgZ+WFVPA0eSfHZRyz2CpmrnXobep2q3TPw6k3wY+A7whar66wJ3W7SJd1FVL1bVc8BXgPWq+v4C91ukId//68CnR+cneRj7jobcxQeBv4/Om8AHFrDXo2qqdu5l6H2qdsuQu/ga8BHgtSS/TvKNRS+5IEPu4r1i4l1U1evA3SS/Bd6qqjf3Yc9FGPJ98QPgpSSvA4/Ttxf/JsnHd9tOH5iSpOZ8YEqSmjP0ktScoZek5gy9JDVn6CWpOUMvSc0Zeklq7p+qJpCl90mYLAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "def computeCost(X, y, theta):\n",
    "\t#计算成本函数J的值``\n",
    "    m = len(y)\n",
    "    J = np.sum(np.power((X*theta - y), 2)) / (2 * m)\n",
    "    return J\n",
    "\n",
    "def gradientDescent(X, y, theta, alpha, num_iters):\n",
    "\t#梯度下降法，得到最终的theta值，并将每次迭代后的J值保留在J_history中。\n",
    "    m = len(y)\n",
    "    J_history = np.mat(np.zeros((num_iters, 1)))\n",
    "    for i in range(num_iters):\n",
    "       theta = theta - alpha * X.T * (X * theta - y) / m\n",
    "       J_history[i] = computeCost(X, y, theta)   \n",
    "    return [theta, J_history]\n",
    "\n",
    "## Part 1: Ploting Data\n",
    "print('Ploting Data...\\n')\n",
    "filename = '../data/ex1data1.txt'\n",
    "\n",
    "data = pd.read_csv(filename, header = None, names = ['x1', 'y'])\n",
    "data.plot.scatter('x1', 'y')\n",
    "plt.xlabel('Population of City in 10,000s')\n",
    "plt.ylabel('Profit in $10,000s')\n",
    "plt.show()\n",
    "\n",
    "## Part 2: Cost and Gradient descent\n",
    "data.insert(0, 'x0', 1) #向数据添加为1的整数列\n",
    "X = data.iloc[:, :-1] #得到变量X \n",
    "y = data.iloc[:, -1] #得到变量y \n",
    "\n",
    "X = np.mat(X)\n",
    "y = np.mat(y) #将X, y变为矩阵形式\n",
    "\n",
    "#设置一些初始参数\n",
    "theta = np.mat(np.zeros((2, 1)))\n",
    "iterations = 1500\n",
    "alpha = 0.01\n",
    "\n",
    "print('Running Gradient Descent...\\n')\n",
    "[theta, J_history] = gradientDescent(X, y, theta, alpha, iterations)\n",
    "print('Theta found by gradient descent:\\n', theta,'\\n')\n",
    "\n",
    "\n",
    "# plot the linear fit\n",
    "plt.plot(X[:,1], y, 'bo', markersize = 4)\n",
    "plt.xlabel('Population of City in 10,000s')\n",
    "plt.ylabel('Profit in $10,000s')\n",
    "plt.plot(X[:,1], X * theta, 'r-')\n",
    "plt.legend(('Training data', 'Linear regression'))\n",
    "plt.show()\n",
    "\n",
    "\n",
    "## Part 3: Visualizing J(theta_0, theta_1)\n",
    "print('Visualizing J(theta_0, theta_1)...\\n')\n",
    "\n",
    "theta0_vals = np.linspace(-10, 10, 100)\n",
    "theta1_vals = np.linspace(-1, 4, 100)\n",
    "\n",
    "J_vals = np.zeros((len(theta0_vals), len(theta1_vals)))\n",
    "\n",
    "for i in range(len(theta0_vals)):\n",
    "    for j in range(len(theta1_vals)):\n",
    "        t = np.vstack((theta0_vals[i], theta1_vals[j]))\n",
    "        J_vals[i,j] = computeCost(X, y, t)\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "ax1 = Axes3D(fig)\n",
    "ax1.plot_surface(theta0_vals, theta1_vals, J_vals, cmap = 'rainbow')\n",
    "plt.xlabel('theta_0')\n",
    "plt.ylabel('theta_1')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.contour(theta0_vals, theta1_vals, J_vals.T, levels = np.logspace(-2, 3, 20))\n",
    "plt.plot(theta[0], theta[1], 'rx', markersize = 10, linewidth = 2)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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